Star Coloring of Subcubic Graphs

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A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on 4 vertices is bi-colored. The star chromatic number of G, χs(G), is the minimum number of colors needed to star color G. In this paper, we show that if a graph G is either non-regular subcubic or cubic with girth at least 6, then χs(G) ≤ 6, and the bound can be realized in linear time.

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@article{T2013, abstract = {A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on 4 vertices is bi-colored. The star chromatic number of G, χs(G), is the minimum number of colors needed to star color G. In this paper, we show that if a graph G is either non-regular subcubic or cubic with girth at least 6, then χs(G) ≤ 6, and the bound can be realized in linear time.}, author = {T. Karthick, C.R. Subramanian}, journal = {Discussiones Mathematicae Graph Theory}, keywords = {vertex coloring; star coloring; subcubic graphs}, language = {eng}, number = {2}, pages = {373-385}, title = {Star Coloring of Subcubic Graphs}, url = {http://eudml.org/doc/268043}, volume = {33}, year = {2013},}

TY - JOURAU - T. KarthickAU - C.R. SubramanianTI - Star Coloring of Subcubic GraphsJO - Discussiones Mathematicae Graph TheoryPY - 2013VL - 33IS - 2SP - 373EP - 385AB - A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on 4 vertices is bi-colored. The star chromatic number of G, χs(G), is the minimum number of colors needed to star color G. In this paper, we show that if a graph G is either non-regular subcubic or cubic with girth at least 6, then χs(G) ≤ 6, and the bound can be realized in linear time.LA - engKW - vertex coloring; star coloring; subcubic graphsUR - http://eudml.org/doc/268043ER -